El modelo de fijación de precios de activos de capital (CAPM, por sus siglas en inglés) indica cuál debería ser la tasa de rendimiento esperada o requerida en activos de riesgo como las acciones ordinarias de Express Scripts.
Tasas de retorno
Express Scripts Holding Co. (ESRX) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Fecha | PrecioESRX,t1 | DividendoESRX,t1 | RESRX,t2 | PrecioS&P 500,t | RS&P 500,t3 |
31 ene. 2013 | $53.42 | 1,498.11 | ||||
1. | 28 feb. 2013 | $56.93 | 6.57% | 1,514.68 | 1.11% | |
2. | 31 mar. 2013 | $57.62 | 1.21% | 1,569.19 | 3.60% | |
3. | 30 abr. 2013 | $59.37 | 3.04% | 1,597.57 | 1.81% | |
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58. | 30 nov. 2017 | $65.18 | 6.35% | 2,647.58 | 2.81% | |
59. | 31 dic. 2017 | $74.64 | 14.51% | 2,673.61 | 0.98% | |
Promedio (R): | 0.73% | 1.02% | ||||
Desviación estándar: | 5.71% | 2.71% |
Express Scripts Holding Co. (ESRX) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Fecha | PrecioESRX,t1 | DividendoESRX,t1 | RESRX,t2 | PrecioS&P 500,t | RS&P 500,t3 |
31 ene. 2013 | $53.42 | 1,498.11 | ||||
1. | 28 feb. 2013 | $56.93 | 6.57% | 1,514.68 | 1.11% | |
2. | 31 mar. 2013 | $57.62 | 1.21% | 1,569.19 | 3.60% | |
3. | 30 abr. 2013 | $59.37 | 3.04% | 1,597.57 | 1.81% | |
4. | 31 may. 2013 | $62.12 | 4.63% | 1,630.74 | 2.08% | |
5. | 30 jun. 2013 | $61.74 | -0.61% | 1,606.28 | -1.50% | |
6. | 31 jul. 2013 | $65.55 | 6.17% | 1,685.73 | 4.95% | |
7. | 31 ago. 2013 | $63.88 | -2.55% | 1,632.97 | -3.13% | |
8. | 30 sept. 2013 | $61.80 | -3.26% | 1,681.55 | 2.97% | |
9. | 31 oct. 2013 | $62.52 | 1.17% | 1,756.54 | 4.46% | |
10. | 30 nov. 2013 | $67.35 | 7.73% | 1,805.81 | 2.80% | |
11. | 31 dic. 2013 | $70.24 | 4.29% | 1,848.36 | 2.36% | |
12. | 31 ene. 2014 | $74.69 | 6.34% | 1,782.59 | -3.56% | |
13. | 28 feb. 2014 | $75.31 | 0.83% | 1,859.45 | 4.31% | |
14. | 31 mar. 2014 | $75.09 | -0.29% | 1,872.34 | 0.69% | |
15. | 30 abr. 2014 | $66.58 | -11.33% | 1,883.95 | 0.62% | |
16. | 31 may. 2014 | $71.47 | 7.34% | 1,923.57 | 2.10% | |
17. | 30 jun. 2014 | $69.33 | -2.99% | 1,960.23 | 1.91% | |
18. | 31 jul. 2014 | $69.65 | 0.46% | 1,930.67 | -1.51% | |
19. | 31 ago. 2014 | $73.93 | 6.15% | 2,003.37 | 3.77% | |
20. | 30 sept. 2014 | $70.63 | -4.46% | 1,972.29 | -1.55% | |
21. | 31 oct. 2014 | $76.82 | 8.76% | 2,018.05 | 2.32% | |
22. | 30 nov. 2014 | $83.15 | 8.24% | 2,067.56 | 2.45% | |
23. | 31 dic. 2014 | $84.67 | 1.83% | 2,058.90 | -0.42% | |
24. | 31 ene. 2015 | $80.71 | -4.68% | 1,994.99 | -3.10% | |
25. | 28 feb. 2015 | $84.79 | 5.06% | 2,104.50 | 5.49% | |
26. | 31 mar. 2015 | $86.77 | 2.34% | 2,067.89 | -1.74% | |
27. | 30 abr. 2015 | $86.40 | -0.43% | 2,085.51 | 0.85% | |
28. | 31 may. 2015 | $87.14 | 0.86% | 2,107.39 | 1.05% | |
29. | 30 jun. 2015 | $88.94 | 2.07% | 2,063.11 | -2.10% | |
30. | 31 jul. 2015 | $90.07 | 1.27% | 2,103.84 | 1.97% | |
31. | 31 ago. 2015 | $83.60 | -7.18% | 1,972.18 | -6.26% | |
32. | 30 sept. 2015 | $80.96 | -3.16% | 1,920.03 | -2.64% | |
33. | 31 oct. 2015 | $86.38 | 6.69% | 2,079.36 | 8.30% | |
34. | 30 nov. 2015 | $85.48 | -1.04% | 2,080.41 | 0.05% | |
35. | 31 dic. 2015 | $87.41 | 2.26% | 2,043.94 | -1.75% | |
36. | 31 ene. 2016 | $71.87 | -17.78% | 1,940.24 | -5.07% | |
37. | 29 feb. 2016 | $70.38 | -2.07% | 1,932.23 | -0.41% | |
38. | 31 mar. 2016 | $68.69 | -2.40% | 2,059.74 | 6.60% | |
39. | 30 abr. 2016 | $73.73 | 7.34% | 2,065.30 | 0.27% | |
40. | 31 may. 2016 | $75.55 | 2.47% | 2,096.95 | 1.53% | |
41. | 30 jun. 2016 | $75.80 | 0.33% | 2,098.86 | 0.09% | |
42. | 31 jul. 2016 | $76.07 | 0.36% | 2,173.60 | 3.56% | |
43. | 31 ago. 2016 | $72.70 | -4.43% | 2,170.95 | -0.12% | |
44. | 30 sept. 2016 | $70.53 | -2.98% | 2,168.27 | -0.12% | |
45. | 31 oct. 2016 | $67.40 | -4.44% | 2,126.15 | -1.94% | |
46. | 30 nov. 2016 | $75.88 | 12.58% | 2,198.81 | 3.42% | |
47. | 31 dic. 2016 | $68.79 | -9.34% | 2,238.83 | 1.82% | |
48. | 31 ene. 2017 | $68.88 | 0.13% | 2,278.87 | 1.79% | |
49. | 28 feb. 2017 | $70.65 | 2.57% | 2,363.64 | 3.72% | |
50. | 31 mar. 2017 | $65.91 | -6.71% | 2,362.72 | -0.04% | |
51. | 30 abr. 2017 | $61.34 | -6.93% | 2,384.20 | 0.91% | |
52. | 31 may. 2017 | $59.75 | -2.59% | 2,411.80 | 1.16% | |
53. | 30 jun. 2017 | $63.84 | 6.85% | 2,423.41 | 0.48% | |
54. | 31 jul. 2017 | $62.64 | -1.88% | 2,470.30 | 1.93% | |
55. | 31 ago. 2017 | $62.82 | 0.29% | 2,471.65 | 0.05% | |
56. | 30 sept. 2017 | $63.32 | 0.80% | 2,519.36 | 1.93% | |
57. | 31 oct. 2017 | $61.29 | -3.21% | 2,575.26 | 2.22% | |
58. | 30 nov. 2017 | $65.18 | 6.35% | 2,647.58 | 2.81% | |
59. | 31 dic. 2017 | $74.64 | 14.51% | 2,673.61 | 0.98% | |
Promedio (R): | 0.73% | 1.02% | ||||
Desviación estándar: | 5.71% | 2.71% |
Mostrar todo
1 Datos en dólares estadounidenses por acción ordinaria, ajustados por divisiones y dividendos de acciones.
2 Tasa de rendimiento de las acciones ordinarias de ESRX durante el período t.
3 Tasa de rendimiento del S&P 500 (el proxy de la cartera de mercado) durante el período t.
Varianza y covarianza
t | Fecha | RESRX,t | RS&P 500,t | (RESRX,t–RESRX)2 | (RS&P 500,t–RS&P 500)2 | (RESRX,t–RESRX)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | 28 feb. 2013 | 6.57% | 1.11% | 34.11 | 0.01 | 0.49 |
2. | 31 mar. 2013 | 1.21% | 3.60% | 0.23 | 6.64 | 1.24 |
3. | 30 abr. 2013 | 3.04% | 1.81% | 5.32 | 0.62 | 1.81 |
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58. | 30 nov. 2017 | 6.35% | 2.81% | 31.54 | 3.19 | 10.03 |
59. | 31 dic. 2017 | 14.51% | 0.98% | 189.98 | 0.00 | -0.54 |
Total (Σ): | 1,888.17 | 424.45 | 388.57 |
t | Fecha | RESRX,t | RS&P 500,t | (RESRX,t–RESRX)2 | (RS&P 500,t–RS&P 500)2 | (RESRX,t–RESRX)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | 28 feb. 2013 | 6.57% | 1.11% | 34.11 | 0.01 | 0.49 |
2. | 31 mar. 2013 | 1.21% | 3.60% | 0.23 | 6.64 | 1.24 |
3. | 30 abr. 2013 | 3.04% | 1.81% | 5.32 | 0.62 | 1.81 |
4. | 31 may. 2013 | 4.63% | 2.08% | 15.22 | 1.11 | 4.11 |
5. | 30 jun. 2013 | -0.61% | -1.50% | 1.80 | 6.36 | 3.39 |
6. | 31 jul. 2013 | 6.17% | 4.95% | 29.60 | 15.40 | 21.35 |
7. | 31 ago. 2013 | -2.55% | -3.13% | 10.75 | 17.24 | 13.61 |
8. | 30 sept. 2013 | -3.26% | 2.97% | 15.89 | 3.81 | -7.78 |
9. | 31 oct. 2013 | 1.17% | 4.46% | 0.19 | 11.81 | 1.49 |
10. | 30 nov. 2013 | 7.73% | 2.80% | 48.93 | 3.18 | 12.47 |
11. | 31 dic. 2013 | 4.29% | 2.36% | 12.68 | 1.78 | 4.75 |
12. | 31 ene. 2014 | 6.34% | -3.56% | 31.42 | 20.98 | -25.67 |
13. | 28 feb. 2014 | 0.83% | 4.31% | 0.01 | 10.82 | 0.33 |
14. | 31 mar. 2014 | -0.29% | 0.69% | 1.05 | 0.11 | 0.34 |
15. | 30 abr. 2014 | -11.33% | 0.62% | 145.53 | 0.16 | 4.85 |
16. | 31 may. 2014 | 7.34% | 2.10% | 43.75 | 1.17 | 7.15 |
17. | 30 jun. 2014 | -2.99% | 1.91% | 13.87 | 0.78 | -3.29 |
18. | 31 jul. 2014 | 0.46% | -1.51% | 0.07 | 6.40 | 0.68 |
19. | 31 ago. 2014 | 6.15% | 3.77% | 29.32 | 7.53 | 14.85 |
20. | 30 sept. 2014 | -4.46% | -1.55% | 26.98 | 6.62 | 13.37 |
21. | 31 oct. 2014 | 8.76% | 2.32% | 64.54 | 1.68 | 10.43 |
22. | 30 nov. 2014 | 8.24% | 2.45% | 56.39 | 2.05 | 10.75 |
23. | 31 dic. 2014 | 1.83% | -0.42% | 1.20 | 2.08 | -1.58 |
24. | 31 ene. 2015 | -4.68% | -3.10% | 29.24 | 17.03 | 22.31 |
25. | 28 feb. 2015 | 5.06% | 5.49% | 18.70 | 19.95 | 19.32 |
26. | 31 mar. 2015 | 2.34% | -1.74% | 2.58 | 7.63 | -4.43 |
27. | 30 abr. 2015 | -0.43% | 0.85% | 1.34 | 0.03 | 0.20 |
28. | 31 may. 2015 | 0.86% | 1.05% | 0.02 | 0.00 | 0.00 |
29. | 30 jun. 2015 | 2.07% | -2.10% | 1.78 | 9.76 | -4.17 |
30. | 31 jul. 2015 | 1.27% | 1.97% | 0.29 | 0.91 | 0.51 |
31. | 31 ago. 2015 | -7.18% | -6.26% | 62.63 | 53.00 | 57.62 |
32. | 30 sept. 2015 | -3.16% | -2.64% | 15.12 | 13.44 | 14.26 |
33. | 31 oct. 2015 | 6.69% | 8.30% | 35.57 | 52.94 | 43.40 |
34. | 30 nov. 2015 | -1.04% | 0.05% | 3.14 | 0.94 | 1.72 |
35. | 31 dic. 2015 | 2.26% | -1.75% | 2.33 | 7.70 | -4.24 |
36. | 31 ene. 2016 | -17.78% | -5.07% | 342.57 | 37.16 | 112.83 |
37. | 29 feb. 2016 | -2.07% | -0.41% | 7.86 | 2.06 | 4.02 |
38. | 31 mar. 2016 | -2.40% | 6.60% | 9.81 | 31.10 | -17.46 |
39. | 30 abr. 2016 | 7.34% | 0.27% | 43.65 | 0.57 | -4.97 |
40. | 31 may. 2016 | 2.47% | 1.53% | 3.02 | 0.26 | 0.89 |
41. | 30 jun. 2016 | 0.33% | 0.09% | 0.16 | 0.87 | 0.37 |
42. | 31 jul. 2016 | 0.36% | 3.56% | 0.14 | 6.44 | -0.95 |
43. | 31 ago. 2016 | -4.43% | -0.12% | 26.63 | 1.31 | 5.90 |
44. | 30 sept. 2016 | -2.98% | -0.12% | 13.80 | 1.31 | 4.26 |
45. | 31 oct. 2016 | -4.44% | -1.94% | 26.71 | 8.79 | 15.32 |
46. | 30 nov. 2016 | 12.58% | 3.42% | 140.45 | 5.74 | 28.39 |
47. | 31 dic. 2016 | -9.34% | 1.82% | 101.49 | 0.64 | -8.04 |
48. | 31 ene. 2017 | 0.13% | 1.79% | 0.36 | 0.59 | -0.46 |
49. | 28 feb. 2017 | 2.57% | 3.72% | 3.38 | 7.28 | 4.96 |
50. | 31 mar. 2017 | -6.71% | -0.04% | 55.35 | 1.13 | 7.90 |
51. | 30 abr. 2017 | -6.93% | 0.91% | 58.74 | 0.01 | 0.87 |
52. | 31 may. 2017 | -2.59% | 1.16% | 11.04 | 0.02 | -0.45 |
53. | 30 jun. 2017 | 6.85% | 0.48% | 37.39 | 0.29 | -3.31 |
54. | 31 jul. 2017 | -1.88% | 1.93% | 6.81 | 0.83 | -2.38 |
55. | 31 ago. 2017 | 0.29% | 0.05% | 0.20 | 0.94 | 0.43 |
56. | 30 sept. 2017 | 0.80% | 1.93% | 0.00 | 0.82 | 0.06 |
57. | 31 oct. 2017 | -3.21% | 2.22% | 15.50 | 1.43 | -4.71 |
58. | 30 nov. 2017 | 6.35% | 2.81% | 31.54 | 3.19 | 10.03 |
59. | 31 dic. 2017 | 14.51% | 0.98% | 189.98 | 0.00 | -0.54 |
Total (Σ): | 1,888.17 | 424.45 | 388.57 |
Mostrar todo
VarianzaESRX = Σ(RESRX,t–RESRX)2 ÷ (59 – 1)
= 1,888.17 ÷ (59 – 1)
= 32.55
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 424.45 ÷ (59 – 1)
= 7.32
CovarianzaESRX, S&P 500 = Σ(RESRX,t–RESRX)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 388.57 ÷ (59 – 1)
= 6.70
Estimación sistemática del riesgo (β)
VarianzaESRX | 32.55 |
VarianzaS&P 500 | 7.32 |
CovarianzaESRX, S&P 500 | 6.70 |
Coeficiente de correlaciónESRX, S&P 5001 | 0.43 |
βESRX2 | 0.92 |
αESRX3 | -0.21% |
Cálculos
1 Coeficiente de correlaciónESRX, S&P 500
= CovarianzaESRX, S&P 500 ÷ (Desviación estándarESRX × Desviación estándarS&P 500)
= 6.70 ÷ (5.71% × 2.71%)
= 0.43
2 βESRX
= CovarianzaESRX, S&P 500 ÷ VarianzaS&P 500
= 6.70 ÷ 7.32
= 0.92
3 αESRX
= PromedioESRX – βESRX × PromedioS&P 500
= 0.73% – 0.92 × 1.02%
= -0.21%
Tasa de rendimiento esperada
Suposiciones | ||
Tasa de rendimiento del LT Treasury Composite1 | RF | 4.67% |
Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 13.79% |
Riesgo sistemático de Express Scripts acciones ordinarias | βESRX | 0.92 |
Tasa de rendimiento esperada de las acciones ordinarias de Express Scripts3 | E(RESRX) | 13.02% |
1 Promedio no ponderado de los rendimientos de las ofertas de todos los bonos del Tesoro de EE. UU. con cupón fijo en circulación que no vencen ni son rescatables en menos de 10 años (proxy de tasa de rendimiento libre de riesgo).
3 E(RESRX) = RF + βESRX [E(RM) – RF]
= 4.67% + 0.92 [13.79% – 4.67%]
= 13.02%